Theorems · Definition · category theory
CategoryTheory.ComposableArrows.precomp
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{n : ℕ} →
(F : CategoryTheory.ComposableArrows C n) → {X : C} → (X ⟶ F.left) → CategoryTheory.ComposableArrows C (n + 1)"Precomposition" of F : ComposableArrows C n by a morphism f : X ⟶ F.left.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ComposableArrowsstatement and proof · cited by 627
- CategoryTheory.ComposableArrows.leftstatement and proof · cited by 40
- CategoryTheory.ComposableArrows.Precomp.objproof · cited by 22
- CategoryTheory.ComposableArrows.Precomp.mapproof · cited by 13
- CategoryTheory.ComposableArrows.Precomp.map_idproof · cited by 0
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.ComposableArrows.mk₂proof · cited by 79
- CategoryTheory.ComposableArrows.mk₃proof · cited by 50
- CategoryTheory.ComposableArrows.precomp_mapstatement and proof · cited by 4
- CategoryTheory.ComposableArrows.mk₄proof · cited by 3
- CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_existsproof · cited by 1
- CategoryTheory.ComposableArrows.precomp_surjectivestatement · cited by 1
- CategoryTheory.ComposableArrows.mk₅proof · cited by 1
- CategoryTheory.ComposableArrows.precomp_objstatement and proof · cited by 0
- CategoryTheory.ComposableArrows.precomp_δ₀statement · cited by 0
- CategoryTheory.Nerve.strictSegalproof · cited by 0